CN113255249B - Multi-physical coupling transient calculation method and device for heat pipe solid state stack - Google Patents

Multi-physical coupling transient calculation method and device for heat pipe solid state stack Download PDF

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CN113255249B
CN113255249B CN202110633723.5A CN202110633723A CN113255249B CN 113255249 B CN113255249 B CN 113255249B CN 202110633723 A CN202110633723 A CN 202110633723A CN 113255249 B CN113255249 B CN 113255249B
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王侃
李泽光
郭玉川
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Tsinghua University
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Abstract

The invention provides a multi-physical coupling transient calculation method for a heat pipe solid state stack, which relates to the technical field of transient calculation of the heat pipe solid state stack, wherein the method comprises the following steps: on the OpenFOAM program, calculating a reactivity feedback model to obtain total reactivity; calling a point stack dynamics model to obtain a power time change function; RMC calculates and obtains the spatial distribution function of the power, upgrade the power description function; determining reactor core power distribution, calculating by a heat pipe transient calculation model to obtain reactor core temperature distribution, and obtaining a reactor core thermal expansion calculation result; judging whether the reactor core is contacted with the reflecting layer or not according to the thermal expansion calculation result; the reactor core heat leakage model calculates and determines the heat leakage quantity between the reactor core, the reflecting layer and the environment; and circularly calling the module until the relative deviation of the peak temperature of the calculation domain of the two iterations is less than 1 e-5. The method solves the problem of accurate coupling calculation of the heat pipe solid-state reactor, can realize transient calculation capability and accident analysis of the heat pipe solid-state reactor, and can be used as an effective tool for designing the reactor core of the heat pipe solid-state reactor.

Description

Multi-physical coupling transient calculation method and device for heat pipe solid state stack
Technical Field
The application relates to the technical field of transient calculation of a heat pipe solid state stack, in particular to a multi-physical coupling transient calculation method and computer equipment for the heat pipe solid state stack.
Background
Unlike a conventional pressurized water reactor, three typical physical processes of neutron transport, core heat transfer and fuel thermal expansion exist in a heat pipe solid state reactor. Aiming at transient calculation of the heat pipe solid-state reactor, the existing scheme is mostly a simplified modeling method based on a single-channel model, a multi-channel model or a lumped parameter model, important processes such as contact heat transfer, reactor core heat leakage, heat pipe power reactivity feedback and the like existing in the heat pipe reactor are ignored, and only preliminary coupling calculation of the heat pipe solid-state reactor can be realized. The spatial distribution characteristics of the fuel temperature are determined by the scattered arrangement of the heat pipes in the stack, and the modeling difficulty can be effectively reduced by adopting a modeling method based on a single-channel model, a multi-channel model or a lumped parameter model, but the real fuel temperature distribution and the peak temperature change cannot be obtained. Meanwhile, the macroscopic distribution of the alkali metal working medium in the heat pipe can be changed by the change of the heat absorption power of the heat pipe, so that reactivity feedback is introduced into the reactor, the reactor power change obtained by calculation is far deviated from the actual state by neglecting the effect, and the real simulation of the dynamic response of the reactor cannot be realized. In addition, the solid core design makes contact heat exchange caused by material thermal expansion become important, and the transformation of a heat transfer model between materials can realize more efficient heat transfer. In the existing technical scheme, the important processes are hardly considered, and the response characteristics of the heat pipe stack in the transient process and the accident condition cannot be truly reflected by the calculation result.
Disclosure of Invention
The present application is directed to solving, at least to some extent, one of the technical problems in the related art.
Therefore, a first objective of the present application is to provide a multiple physical coupling transient calculation method for a heat pipe solid state stack, which solves the technical problem that the real fuel temperature distribution and peak temperature change cannot be obtained by using a simplified modeling method based on a single-channel model, a multi-channel model or a lumped parameter model in the existing method, and also solves the problem that the response characteristics of the heat pipe stack in the transient process and the accident condition cannot be truly reflected in the calculation result because important processes such as contact heat transfer, core heat leakage, heat pipe power reactivity feedback and the like existing in the heat pipe stack are ignored in the existing method. According to the method, the important structures such as the reactor core, the heat pipe and the reflecting layer are accurately modeled, and the important processes such as fuel heat transfer, heat absorption of the heat pipe, heat leakage of the reactor core, fuel expansion, feedback of an expansion reactor, power reactivity feedback and the like existing in the heat pipe reactor are carefully considered, so that the fine simulation of the transient behavior of the heat pipe solid state reactor is realized.
A second object of the present application is to propose a computer device.
A third object of the present application is to propose a non-transitory computer-readable storage medium.
To achieve the above object, an embodiment of a first aspect of the present application provides a method for multiple physically coupled transient state calculation for a heat pipe solid state stack, including: the method is characterized in that an OpenFOAM program is used as a platform, a reactivity feedback model, a point reactor dynamics model, a heat pipe transient calculation model, a contact heat exchange model and a reactor core heat leakage model are subjected to modular design, and multi-coupling physical calculation of the heat pipe solid state reactor is realized through calling and iteration among different modules, wherein the calling and iteration among the different modules comprise the following steps:
inputting the temperature distribution of the current reactor and the heat absorption power of the heat pipe as input data into a reactivity feedback model for reactivity feedback calculation to obtain the total reactivity at the current moment;
calling a point reactor dynamics model, and obtaining a power time change function according to the total reactivity;
calculating according to RMC to obtain a power spatial distribution function, and updating the current power description function according to the power spatial distribution function and the power time change function to obtain an updated power description function;
determining the reactor core power distribution at the current moment by using the updated power description function, calling a heat pipe transient calculation model to perform heat transfer coupling calculation on the reactor core to obtain the reactor core temperature distribution, bringing the reactor core temperature distribution into a deformation equation containing thermal expansion, and calculating to obtain the reactor core thermal expansion calculation result;
judging whether the reactor core is in contact with the reflecting layer or not according to the thermal expansion calculation result of the reactor core, calling a contact heat exchange model to perform heat transfer calculation between the reactor core and the reflecting layer if the reactor core is in contact with the reflecting layer, obtaining a corresponding contact heat exchange coefficient, and updating the heat transfer quantity between the reactor core and the reflecting layer by combining the outer surface temperature of the reactor core and the inner surface temperature of the reflecting layer on the basis of the contact heat exchange coefficient; (ii) a
Inputting the heat transfer quantity between the reactor core and the reflecting layer into a reactor core heat leakage model as input data to calculate the heat leakage of the reflecting layer, thereby determining the heat leakage quantity between the reactor core, the reflecting layer and the environment;
and (4) calling and iterating different modules in a circulating manner until the relative deviation of the peak temperature of the calculation domain of the two iterations is less than 1 e-5.
Optionally, in an embodiment of the present application, the reactive feedback calculation is specifically expressed as:
ρ(t)＝ρ0+ρext+ρD+ρF+ρH1+ρH2+ρS
Figure BDA0003104745010000021
ρH2＝αH2[Q(t)-Q(0)]，ρS＝αs[Tm(t)-Tm(0)]
where ρ is0For initial reactivity, pextFor external introduction of reactivity, pDFor fuel Doppler feedback reactivity, ρFFor deformation feedback reactivity, ρH1For heat pipe temperature feedback reactivity, ρH2For heat pipe power feedback reactivity, ρSFor temperature feedback reactivity of the structural material, alphaD、αF、
Figure BDA0003104745010000022
αsIs the reactive feedback coefficient.
Optionally, in one embodiment of the present application, the point stack dynamics model includes a system of point stack dynamics equations expressed as:
Figure BDA0003104745010000023
Figure BDA0003104745010000031
Figure BDA0003104745010000032
wherein rho is total reactivity, beta is effective fraction of delayed neutrons, lambda is average generation time of prompt neutrons, and lambdaiIs the decay constant of the precursor nucleus, C, of each group of delayed neutronsiPrecursor nuclear density, beta, of each group of delayed neutronsiFor each group of delayed neutrons to be effectiveAnd (4) shares.
Optionally, in an embodiment of the present application, the current power description function is updated according to a power spatial distribution function and a power time variation function, which is expressed as:
P(r,t)＝K(r)×p(t)
wherein p (t) is a power time variation function, K (r) is a power space distribution function, r is a space coordinate, and t is time.
Optionally, in an embodiment of the present application, the heat pipe transient calculation model includes a self-diffusion model, a plane front model, and a network thermal resistance model, the starting of the heat pipe is divided into 3 stages, and different heat pipe transient calculation models are called to perform heat transfer coupling calculation on the core according to the difference of the stages, where the judgment of the different stages is performed by using a Kundsen number, where the Kundsen number is expressed as:
Figure BDA0003104745010000033
wherein, the lambda is the calculation formula of the mean free path of the steam molecules,
Figure BDA0003104745010000034
d is the pipe diameter, TtrFor the transition temperature, the transition temperature T under different Kn numbers and pipe diameters D is calculated on the premise that the steam cavity working medium is in a saturated statetrK is a Boltzmann function, P is a pressure, σ is an average collision diameter of gas molecules,
when Kn is more than or equal to 0.01, calling a self-diffusion model in the heat pipe transient calculation model;
when Kn is less than 0.01 and the heat pipe is not completely started, calling a plane front heat pipe model in the heat pipe transient calculation model;
and when Kn is less than 0.01 and the heat pipe is completely started, calling a network thermal resistance model in the heat pipe transient calculation model.
Alternatively, in one embodiment of the present application, the heat transfer between the core and the reflector is calculated as:
Figure BDA0003104745010000035
Figure BDA0003104745010000036
wherein HiIs the hardness of the material, kiIs the thermal conductivity, σiTo surface roughness, miIs the slope of the surface roughness peak, P is the contact pressure, dbIs the coefficient of the Vickers microhardness relation, hcTo contact heat transfer coefficient, HbIs the equivalent hardness of the material, H1Material 1 hardness, H2Is the hardness, k, of material 21Is the thermal conductivity, k, of the material 12Is the thermal conductivity, k, of material 2sTo equivalent thermal conductivity, σ1Is the surface roughness, σ, of the material 12Is the surface roughness, m, of the material 21The roughness of the surface of the material 1 is the slope of the peak, m2The slope of the roughness peak on the surface of the material 2.
Optionally, in an embodiment of the present application, whether the core is in contact with the reflective layer is determined according to a core thermal expansion calculation result, if the core is not in contact with the reflective layer, heat transfer is achieved between the core and the reflective layer through a radiation heat exchange or gap heat conduction manner, and a steady-state radiation heat exchange formula and a steady-state heat conduction formula under corresponding geometric conditions are used to perform heat transfer calculation.
Optionally, in an embodiment of the present application, the reflective layer leakage heat is calculated by:
Figure BDA0003104745010000041
where ρ is the material density of the reflective layer, cpThe specific heat capacity of the reflecting layer material is adopted, k is the material heat conductivity, Q is the volume heat source of the reflecting layer, T is the material temperature, the inner surface of the reflecting layer uses clearance heat transfer or contact heat transfer to calculate the heat flow between the reactor core and the reflecting layer, and the outer surface adopts a convection heat transfer boundary or a radiation heat transfer boundary according to the actual reactor.
To achieve the above object, a second embodiment of the present invention provides a computer device, including: the device comprises a memory, a processor and a computer program stored on the memory and capable of running on the processor, wherein the processor realizes the multi-physical coupling transient calculation method for the heat pipe solid-state stack when executing the computer program.
To achieve the above object, a non-transitory computer readable storage medium capable of executing a multiple physical coupling transient calculation method for a heat pipe solid state stack is provided according to a third embodiment of the present invention.
The multi-physical coupling transient calculation method, the computer device and the non-transitory computer readable storage medium for the heat pipe solid state reactor in the embodiment of the application are based on the independently developed reactor card program RMC and the open source CFD program OpenFOAM, and the method and the device realize the fine simulation of the transient behavior of the heat pipe solid state reactor by accurately modeling important structures such as the reactor core, the heat pipe, the reflecting layer and the like and carefully considering important processes such as fuel heat transfer, heat absorption of the heat pipe, heat leakage of the reactor core, fuel expansion, feedback of the expansion reactor, power reactivity and the like in the heat pipe solid state reactor, so that the problem of accurate coupling calculation of the 'nuclear-heat-force' process of the reactor core of the heat pipe solid state reactor is solved, the transient calculation and the accident analysis of the heat pipe solid state reactor can be realized, and the method and the non-transitory computer readable storage medium can be used as an effective tool for designing the reactor core of the heat pipe solid state reactor.
Additional aspects and advantages of the present application will be set forth in part in the description which follows and, in part, will be obvious from the description, or may be learned by practice of the present application.
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The foregoing and/or additional aspects and advantages of the present application will become apparent and readily appreciated from the following description of the embodiments, taken in conjunction with the accompanying drawings of which:
fig. 1 is a schematic flowchart of a transient calculation method for multiple physical couplings of a heat pipe solid state stack according to an embodiment of the present application;
FIG. 2 is a power distribution update diagram in a multiple physical coupling transient calculation for a heat pipe solid state stack according to an embodiment of the present application;
FIG. 3 is a diagram illustrating distribution changes of working mediums of different heat pipes under different heat absorption powers according to the transient multi-physical coupling calculation method for a heat pipe solid state stack in the embodiment of the present application;
FIG. 4 is a diagram of a contact heat transfer process of material expansion by heating for a multiple physical coupling transient calculation method of a heat pipe solid state stack according to an embodiment of the present application;
FIG. 5 is a general calculation flowchart of a coupling method of a transient calculation method for multiple physical couplings of a heat pipe solid state stack according to an embodiment of the present application;
FIG. 6 is a diagram of a model of a KRUSTY reactor RMC for a multiple physical coupling transient calculation method of a heat pipe solid state stack according to an embodiment of the present disclosure;
FIG. 7 is a diagram of a KRUSTY reactor core OpenFOAM model for a multiple physical coupling transient calculation method for a heat pipe solid state reactor according to an embodiment of the present application;
FIG. 8 is a KRUSTY reactor experimental result chart for a multiple physical coupling transient calculation method of a heat pipe solid state reactor according to an embodiment of the present application;
FIG. 9 is a diagram illustrating a calculation result of a coupling method of a transient calculation method for multiple physical couplings of a heat pipe solid state stack according to an embodiment of the present application;
FIG. 10 is a block diagram of a "nuclear-thermal-force" coupling overall calculation for a multiple physical coupling transient calculation method for a heat pipe solid state stack according to an embodiment of the present application;
fig. 11 is a block diagram of OpenFOAM "thermal-force" coupling calculation for a transient calculation method for multiple physical couplings of a heat pipe solid-state stack according to an embodiment of the present application.
Detailed Description
Reference will now be made in detail to the embodiments of the present application, examples of which are illustrated in the accompanying drawings, wherein like or similar reference numerals refer to the same or similar elements or elements having the same or similar function throughout. The embodiments described below with reference to the drawings are exemplary and intended to be used for explaining the present application and should not be construed as limiting the present application.
The method for calculating the transient state of multiple physical couplings of the heat pipe solid-state stack according to the embodiment of the application is described below with reference to the attached drawings.
Fig. 1 is a schematic flowchart of a transient calculation method for multiple physical couplings of a heat pipe solid state stack according to an embodiment of the present application.
As shown in fig. 1, the method for calculating the transient state of multiple physical couplings of the heat pipe solid state stack includes: the method is characterized in that an OpenFOAM program is used as a platform, a reactivity feedback model, a point reactor dynamics model, a heat pipe transient calculation model, a contact heat exchange model and a reactor core heat leakage model are subjected to modular design, and multi-coupling physical calculation of the heat pipe solid state reactor is realized through calling and iteration among different modules, wherein the calling and iteration among the different modules comprise the following steps:
step 101, inputting the temperature distribution of the current reactor and the heat absorption power of a heat pipe as input data into a reactivity feedback model for reactivity feedback calculation to obtain the total reactivity at the current moment;
step 102, calling a point reactor dynamics model, and obtaining a power time change function according to the total reactivity;
103, calculating according to the RMC to obtain a power spatial distribution function, and updating the current power description function according to the power spatial distribution function and the power time change function to obtain an updated power description function;
104, determining the reactor core power step by step at the current moment by using the updated power description function, calling a heat pipe transient calculation model to perform heat transfer coupling calculation on the reactor core to obtain reactor core temperature distribution, bringing the reactor core temperature distribution into a deformation equation containing thermal expansion, and calculating to obtain a reactor core thermal expansion calculation result;
105, judging whether the reactor core is in contact with the reflecting layer or not according to the thermal expansion calculation result of the reactor core, calling a contact heat exchange model to perform heat transfer calculation between the reactor core and the reflecting layer if the reactor core is in contact with the reflecting layer to obtain a corresponding contact heat exchange coefficient, and updating the heat transfer quantity between the reactor core and the reflecting layer by combining the temperature of the outer surface of the reactor core and the temperature of the inner surface of the reflecting layer on the basis of the contact heat exchange coefficient;
step 106, inputting the heat transfer quantity between the reactor core and the reflecting layer as input data into a reactor core heat leakage model to calculate the heat leakage of the reflecting layer, so as to determine the heat leakage quantity between the reactor core, the reflecting layer and the environment;
and step 107, circularly calling and iterating different modules until the relative deviation of the peak temperature of the calculation domain of the two iterations is less than 1 e-5.
The multi-physical coupling transient calculation method for the heat pipe solid state stack comprises the following steps: the method is characterized in that an OpenFOAM program is used as a platform, a reactivity feedback model, a point reactor dynamics model, a heat pipe transient calculation model, a contact heat exchange model and a reactor core heat leakage model are subjected to modular design, and multi-coupling physical calculation of the heat pipe solid state reactor is realized through calling and iteration among different modules, wherein the calling and iteration among the different modules comprise the following steps: inputting the temperature distribution of the current reactor and the heat absorption power of the heat pipe as input data into a reactivity feedback model for reactivity feedback calculation to obtain the total reactivity at the current moment; calling a point reactor dynamics model, and obtaining a power time change function according to the total reactivity; calculating according to RMC to obtain a power spatial distribution function, and updating the current power description function according to the power spatial distribution function and the power time change function to obtain an updated power description function; determining the reactor core power step by step at the current moment by using the updated power description function, calling a heat pipe transient calculation model to perform heat transfer coupling calculation on the reactor core to obtain the reactor core temperature distribution, bringing the reactor core temperature distribution into a deformation equation containing thermal expansion, and calculating to obtain the reactor core thermal expansion calculation result; judging whether the reactor core is in contact with the reflecting layer or not according to the thermal expansion calculation result, calling a contact heat exchange model to perform heat transfer calculation between the reactor core and the reflecting layer if the reactor core is in contact with the reflecting layer, obtaining a corresponding contact heat exchange coefficient, and updating the heat transfer quantity between the reactor core and the reflecting layer by combining the outer surface temperature of the reactor core and the inner surface temperature of the reflecting layer on the basis of the contact heat exchange coefficient; inputting the heat transfer quantity between the reactor core and the reflecting layer into a reactor core heat leakage model as input data to calculate the heat leakage of the reflecting layer, thereby determining the heat leakage quantity between the reactor core, the reflecting layer and the environment; and (4) calling and iterating different modules in a circulating mode until the relative deviation of the peak temperature of the two iterations is smaller than 1 e-5. Therefore, the method can solve the technical problem that the real fuel temperature distribution and peak temperature change cannot be obtained by adopting a simplified modeling method based on a single-channel model, a multi-channel model or a lumped parameter model in the existing method, and simultaneously solves the problem that the response characteristics of the heat pipe stack under the transient process and the accident condition cannot be truly reflected in the calculation result because important processes such as contact heat transfer, reactor core heat leakage, heat pipe power reactivity feedback and the like in the heat pipe stack are ignored in the existing method. Meanwhile, important processes of fuel heat transfer, heat absorption of the heat pipe, reactor core heat leakage, fuel expansion, feedback of an expansion reactor, feedback of power reactivity and the like in the heat pipe reactor are considered carefully through accurate modeling of important structures such as a reactor core, the heat pipe, a reflecting layer and the like, so that the fine simulation of transient behavior of the heat pipe solid state reactor is realized.
Further, in the embodiment of the present application, the reactive feedback calculation is specifically expressed as:
ρ(t)＝ρ0+ρext+ρD+ρF+ρH1+ρH2+ρS
Figure BDA0003104745010000071
ρH2＝αH2[Q(t)-Q(0)]，ρS＝αs[Tm(t)-Tm(0)]
where ρ is0For initial reactivity, pextFor external introduction of reactivity, pDFor fuel Doppler feedback reactivity, ρFFor deformation feedback reactivity, ρH1For heat pipe temperature feedback reactivity, ρH2For heat pipe power feedback reactivity, ρSFor temperature feedback reactivity of the structural material, alphaD、αF、
Figure BDA0003104745010000072
αsIs the reactive feedback coefficient.
The unique design of the heat pipe solid state reactor eliminates the temperature feedback and cavitation effect of the moderator existing in the pressurized water reactor. But there are fuel deformation reactivity feedback, heat pipe temperature reactivity feedback, and heat pipe power reactivity feedback.
Reactive feedbackCoefficient, e.g. alphaD、αH1And alphaSCan be obtained by modifying the corresponding material temperature in the montage program RMC or using temperature perturbation calculations. For alphaFThe method is calculated by the following steps: selecting the volume average temperature as the characteristic temperature of the fuel, and calculating the expansion of the fuel at different temperatures by using OpenFOAM; counting the surface average deformation of each surface, and regarding the surface average deformation as the actual surface deformation; updating the fuel density according to the surface deformation; updating an RMC model input file according to the surface average deformation and the fuel density; calculating k for different cases using RMCeffObtaining a deformation reactivity feedback coefficient alpha according to the calculated resultF。
Although the reactivity feedback of a single heat pipe is not obvious, a plurality of heat pipes are often present in the core, and the reactivity feedback process needs to be considered. For alphaH2The calculation of (2) can be realized by the following steps: the limit heat transfer power of the heat pipe is calculated by using an empirical formula. Under the limit heat transfer power, the curvature radius of the liquid-gas interface of the liquid absorption core is the capillary radius; considering that the heat absorption power of the heat pipe and the gas-liquid interface depression degree are in a linear relation, and determining the gas-liquid interface radius under different heat absorption powers; in the RMC model, the complex structure of the liquid absorption core is subjected to uniform equivalent treatment, and the description of the change of the working medium in the liquid absorption core is realized by modifying corresponding interface parameters; k was calculated using RMC for different wick thicknesseseffSo as to obtain the power reactivity feedback coefficient alpha of the heat pipeH2。
Further, in the embodiment of the present application, the point stack kinetic model is a point stack kinetic equation set, and the point stack kinetic equation set is expressed as:
Figure BDA0003104745010000073
Figure BDA0003104745010000074
Figure BDA0003104745010000075
wherein rho is total reactivity, beta is effective fraction of delayed neutrons, lambda is average generation time of prompt neutrons, and lambdaiIs the decay constant of the precursor nucleus, C, of each group of delayed neutronsiPrecursor nuclear density, beta, of each group of delayed neutronsiThe effective portion of delayed neutrons in each group.
For the calculation of reactor shutdown decay heat, the total decay power of the reactor core at different times can be obtained by directly using a burnup equation of which the neutron flux of the RMC corresponding to the heat pipe reactor is zero and combining the decay constant and the decay heat release quantity, and then an interpolation algorithm is used for obtaining a change curve of the decay power along with time.
Further, in the embodiment of the present application, the current power description function is updated according to the power spatial distribution function and the power time variation function, and is represented as:
P(r,t)＝K(r)×p(t)
wherein, P (t) is a power time variation function, k (r) is a power space distribution function, r is a space coordinate, t is time, and P (r, t) is a power description function, which represents the relation between power and space and time, therefore, the reactor core power distribution at the current moment can be determined directly according to the updated power description function, and the reactor core heat transfer calculation is performed by using the updated reactor core power distribution.
In the coupling method, a core fission power description function P (r, t) is decomposed into a product form of a space variable K (r) and a time variable P (t), a power space distribution function K (r) is obtained by RMC calculation, and a power time variation function P (t) is obtained by solving a point reactor dynamics equation system comprising 6 groups of delayed neutron precursor cores.
Further, in the embodiment of the present application, the high-temperature heat pipe starting process may be divided into 3 stages, and each stage selects a different heat pipe model to perform the transient behavior simulation of the heat pipe. The models used were respectively: self-diffusion model, plane front model, network thermal resistance model. The heat pipe transient calculation model comprises a self-diffusion model, a plane front model and a network thermal resistance model, wherein the self-diffusion model is used for transient simulation at the initial stage of heat pipe starting, the plane front model is used for transient simulation at the transition stage of heat pipe starting, the network thermal resistance model is used for transient simulation after the heat pipe starting succeeds, the heat of a reactor core is led out by a heat pipe, the heat pipe transient calculation model is called to actually perform coupling calculation between the heat pipe and the reactor core, the temperature distribution of the reactor core is determined by solving a heat conduction differential equation, the heat pipe transient calculation model comprises the self-diffusion model, the plane front model and the network thermal resistance model, the heat pipe starting is divided into 3 stages, different heat pipe transient calculation models are called to perform heat transfer coupling calculation on the reactor core according to the different stages, the heat transfer coupling calculation means that the reactor core and the heat pipe are subjected to heat transfer calculation, and the iteration is required to be performed between the heat transfer calculation of the reactor core and the heat pipe because the reactor core and the heat pipe are directly contacted and mutually influenced, until the convergence of the signals is reached,
wherein, the judgment of different stages adopts Kundsen number to judge, and the Kundsen number is expressed as:
Figure BDA0003104745010000081
wherein, the lambda is the calculation formula of the mean free path of the steam molecules,
Figure BDA0003104745010000082
d is the pipe diameter, TtrFor the transition temperature, the transition temperature T under different Kn numbers and pipe diameters D is calculated on the premise that the steam cavity working medium is in a saturated statetrK is a Boltzmann function, P is a pressure, and σ is an average collision diameter of gas molecules,
when Kn is more than or equal to 0.01, calling a self-diffusion model in the heat pipe transient calculation model;
when Kn is less than 0.01 and the heat pipe is not completely started, calling a plane front heat pipe model in the heat pipe transient calculation model;
and when Kn is less than 0.01 and the heat pipe is completely started, calling a network thermal resistance model in the heat pipe transient calculation model.
The heat pipe solid state stack system adopts an alkali metal heat pipe as a heat conducting component. During the starting and transient operation of the heat pipe, complex physical processes exist, such as the melting and solidification of working media, steam flow, evaporation and condensation of a vapor-liquid interface and the like. In the heat pipe calculation model, the heat pipe operation is divided into 3 stages, and each stage is analyzed by using different models, which specifically comprises the following steps: self-diffusion model, plane front model, network thermal resistance model. The self-diffusion model is used for generating no steam in the steam cavity or in a lean gas flowing stage; the plane front model is used for the flow stage of starting to generate continuous steam in the steam cavity; the network thermal resistance model is applied to the stage when the steam in the steam cavity completely reaches the continuous flow. Judging in different stages by using Knudsen number. For the transition from the self-diffusion flow to the continuous flow of the rarefied steam, a judgment criterion Kn is less than or equal to 0.01 for distinguishing.
The self-diffusion model comprises the following components: a system of thermal conductivity differential equations and self-diffusion equations, as follows:
differential equation of heat conduction:
Figure BDA0003104745010000091
wherein rho is material density, C is material specific heat capacity, lambda is material thermal conductivity, T is material temperature, and T is time.
The self-diffusion equation set comprises a mass self-diffusion equation and an energy self-diffusion equation:
mass self-diffusion equation:
Figure BDA0003104745010000092
energy self-diffusion equation:
Figure BDA0003104745010000093
wherein D isvIs the vapor self-diffusion coefficient, GrFor radially self-diffusing mass flow, GzThe self-diffusion mass flow in the axial direction is shown, r is a radial coordinate, and z is an axial coordinate.
The plane front equation comprises a heat conduction differential equation, and also comprises a fluid continuity equation, an N-S equation and a fluid energy equation:
continuity equation:
Figure BDA0003104745010000094
axial N-S equation:
Figure BDA0003104745010000095
radial N-S equation:
Figure BDA0003104745010000101
energy equation:
Figure BDA0003104745010000102
wherein v is the radial velocity, w is the radial velocity, μ is the steam viscosity, P is the steam pressure, and φ is the energy source term.
The network thermal resistance model uses a node equation to calculate the temperature:
Figure BDA0003104745010000103
where A is the node area, Q is the input/output energy, and i is the node number.
The heat generated by the reactor core is absorbed by the heat pipe, which is the most important way for removing the heat of the reactor core, so that the transient calculation model of the heat pipe is called to calculate the heat transfer of the reactor core and the heat pipe when the heat transfer calculation of the reactor core is carried out. And determining the thermal expansion amount of the reactor core according to the updated temperature of the reactor core.
Further, in the embodiment of the present application, the heat transfer between the core and the reflector is calculated and expressed as:
Figure BDA0003104745010000104
Figure BDA0003104745010000105
wherein HiIs the hardness of the material, kiIs the thermal conductivity, σiTo surface roughness, miIs the slope of the surface roughness peak, P is the contact pressure, dbIs the coefficient of the Vickers microhardness relation, hcTo contact heat transfer coefficient, HbIs the equivalent hardness of the material, H1Material 1 hardness, H2Is the hardness, k, of material 21Is the thermal conductivity, k, of the material 12Is the thermal conductivity, k, of material 2sTo equivalent thermal conductivity, σ1Is the surface roughness, σ, of the material 12Is the surface roughness, m, of the material 21The roughness of the surface of the material 1 is the slope of the peak, m2The slope of the roughness peak on the surface of the material 2.
The properties of the solid core make the contact heat exchange caused by the thermal expansion of the materials important, and the contact heat exchange between the materials is beneficial to the transfer of heat to another material and enables the temperature of the other material to rise rapidly. For contact heat exchange, an empirical relationship proposed by Yovenovich et al is used.
Based on the contact heat exchange coefficient, the heat transfer quantity between the reactor core and the reflecting layer is updated by combining the temperature of the outer surface of the reactor core and the temperature of the inner surface of the reflecting layer, and the heat transfer quantity between the reactor core and the reflecting layer needs to be known, so that the contact heat exchange coefficient (obtained through a contact heat exchange model) needs to be known on one hand, and the temperature of the two surfaces which are in contact needs to be known on the other hand (obtained through heat transfer calculation and statistics), therefore, the heat transfer quantity between the reactor core and the reflecting layer can be updated by taking the contact heat exchange coefficient as the basis.
Further, in the embodiment of the present application, after the thermal expansion calculation is completed, the geometric coordinates of the expanded outer surface of the core can be known, the spatial position of the reflecting layer is known, and by comparing the distance between the expanded core and the reflecting layer, whether the core and the reflecting layer are in contact or not can be known, and whether the core and the reflecting layer are in contact or not can obviously change the heat transfer condition between the core and the reflecting layer, in order to realize accurate coupling calculation, whether the reactor core and the reflecting layer are contacted needs to be judged in real time, and calculating the heat transfer quantity between the reactor core and the reflecting layer according to the judgment result, if the reactor core and the reflecting layer are not contacted, the heat transfer is realized by the radiation heat exchange or the gap heat conduction mode, because the clearance is often smaller, the radiation heat exchange and the clearance heat conduction can directly adopt a steady-state radiation heat exchange formula and a steady-state heat conduction formula under corresponding geometric conditions to carry out heat transfer calculation.
When no contact occurs with the surfaces, the heat transfer calculation will be performed directly using the gap heat transfer model. For the heat pipe stack, the phenomenon that the original non-contact surface is in 'non-contact-close contact' due to thermal expansion is likely to occur, the heat transfer among materials can be greatly changed in the process, so for the multi-physical coupling of the heat pipe stack, the contact heat exchange must be considered, and a relevant model is called to calculate according to the actual contact condition of the materials.
Further, in the embodiment of the present application, the heat leakage of the reflective layer is calculated as:
Figure BDA0003104745010000111
where ρ is the material density of the reflective layer, cpThe specific heat capacity of the reflecting layer material is adopted, k is the material heat conductivity, Q is the volume heat source of the reflecting layer, T is the material temperature, the heat flow between the reactor core and the reflecting layer is calculated by using the gap heat transfer or contact heat exchange on the inner surface of the reflecting layer, and the convection heat exchange boundary or the radiation heat exchange boundary is adopted on the outer surface according to the actual reactor.
Due to the compact nature of the heat pipe solid state stack, core heat transfer through the reflector layer will be an important path for core heat dissipation. The heat transfer mode of the reflecting layer is heat conduction, and the temperature field can be calculated by directly adopting a heat conduction differential equation.
Fig. 2 is a power distribution update diagram in a multiple physical coupling transient calculation for a heat pipe solid state stack according to an embodiment of the present application.
As shown in fig. 2, in the transient calculation method for multiple physical couplings of a heat pipe solid state stack, for some working conditions with obvious power distribution change, such as the rotation of a control rod moving nuclear control drum, during the transient calculation, the coupling calculation between RMC and OpenFOAM is required to update the power spatial distribution function k (r).
Fig. 3 is a working medium distribution change diagram under different heat pipe heat absorption powers of the multiple physical coupling transient calculation method for the heat pipe solid state stack according to the embodiment of the present application.
As shown in FIG. 3, in the multiple physical coupling transient calculation method for the heat pipe solid state stack, when the heat absorbed by the heat pipe is reduced, the evaporation of the working medium is weakened, the curvature radius of a gas-liquid interface is increased, and the accumulation of the working medium in an evaporation section is caused, so that the reactivity feedback is introduced into the stack.
Fig. 4 is a diagram of a contact heat transfer process of material expansion by heating for a multiple physical coupling transient calculation method of a heat pipe solid state stack according to an embodiment of the present application.
As shown in fig. 4, the heat transfer manner between materials of the multiple physical coupling transient calculation method for the heat pipe solid state stack is as follows: the material 1 is heated to a gradually increasing temperature, so that the material continuously expands outwards. When the materials are not contacted, the heat transfer mode between the materials is heat conduction or radiation heat exchange. After the mutual contact occurs, the heat transfer mode is changed into contact heat exchange. The heat transfer from the contact between the materials will be beneficial to the heat transfer to the material 2 and make its temperature rise rapidly.
Fig. 5 is a general calculation flowchart of a coupling method of a multiple physical coupling transient calculation method for a heat pipe solid state stack according to an embodiment of the present application.
As shown in fig. 5, the calculation flow of the coupling method in the multiple physical coupling transient calculation method for the heat pipe solid state stack is as follows:
step 201: according to the temperature distribution of the reactor and the heat absorption power of the heat pipe at the moment, the equation rho (t) is applied to be rho0+ρext+ρD+ρF+ρH1+ρH2+ρSCalculating to obtain the total reactivity at the moment;
step 202: solving a point reactor dynamics equation set to obtain a power time change function p (t);
step 203: updating a power description function P (r, t) at the moment according to the power distribution calculated by the RMC;
step 204: calculating heat transfer and thermal expansion of the reactor core;
step 205: and judging whether the reactor core is in contact with the reflecting layer or not according to the thermal expansion calculation result of the reactor core. If contact occurs, the heat transfer between the two surfaces is contact heat transfer, and the equation is used
Figure BDA0003104745010000121
Calculating to obtain a corresponding contact heat exchange coefficient;
step 206: calculating the heat flux density between the reactor core and the reflecting layer according to the average temperature of the reactor core and the surface of the reflecting layer;
step 207: repeating the calculating steps 204 to 206 until the relative deviation of the peak temperature of the two iterations is less than 1 e-5;
step 208: if the transient calculation is completed, the result post-processing is performed, and if the transient calculation is not completed, the calculation steps 201 to 207 are repeated.
After each calculation, the peak temperature in all calculation domains is counted, and if the relative deviation of the peak temperature is less than 1e-5 in 2 adjacent iterations, the iterations are considered to be converged.
Fig. 6 is a diagram of a model of a KRUSTY reactor RMC for a multiple physical coupling transient calculation method of a heat pipe solid-state stack according to an embodiment of the present disclosure.
As shown in fig. 6, the KRUSTY reactor RMC model of the multiple physical coupling transient calculation method for a heat pipe solid state stack includes a core, a reflector, a heat pipe, a Haynes230 ring, and a shielding layer, omitting a stirling engine, a vacuum chamber, and a platen.
Fig. 7 is a diagram of an OpenFOAM model of a reactor core of a KRUSTY reactor for a multiple physical coupling transient calculation method of a heat pipe solid state reactor according to an embodiment of the present application.
As shown in fig. 7, the KRUSTY reactor core OpenFOAM model of the transient calculation method for multiple physical couplings of a heat pipe solid state reactor models only the core, and couples the heat transfer between the reflector and the heat pipe by using corresponding sub-modules.
FIG. 8 is a graph showing the results of the KRUSTY reactor experiment according to the method for calculating multiple physical coupling transients for a heat pipe solid state reactor of the present application; .
As shown in FIG. 8, the multiple physical coupling transient calculation method for the heat pipe solid state stack selects a typical heat pipe solid state stack KRUSTY (Kiloatt Reactor Using Stirling technology) for verification of the coupling method, selects a load trace of the Reactor with 25% reduction of the absorption power of the Stirling motor for simulation calculation, and sets the motor to reduce the power by 25% to about 2.02kWt in a KRUSTY experiment.
Fig. 9 is a diagram of a calculation result of a coupling method of a multiple physical coupling transient calculation method for a heat pipe solid state stack according to an embodiment of the present application.
In the transient calculation method for multiple physical couplings of the heat pipe solid-state stack, as shown in fig. 9, for transient calculation, the absorbed power of the heat pipe is set to be stepped down to the target value and is kept unchanged all the time, and the calculation result is shown in fig. 9. From the calculation results, the reactivity change, the power change and the average temperature change of the reactor core all accord with the experiment results well, and the calculation correctness of the coupling method is verified.
Fig. 10 is a "core-heat-force" coupling overall calculation block diagram of a multiple physical coupling transient calculation method for a heat pipe solid-state stack according to an embodiment of the present application.
As shown in fig. 10, the transient calculation method for multiple physical couplings of a heat pipe solid state stack is a method research for multiple physical coupling calculations of "nuclear-thermal-force" of the heat pipe solid state stack, and adopts a stack physics monte program RMC to perform neutron transport ("nuclear") calculation, and can obtain reactor power spatial distribution and reactivity feedback coefficients, and adopts a CFD program OpenFOAM to perform process calculations such as core heat transfer and thermal expansion, heat pipe heat transfer, heat leakage of a reflective layer, and the like.
Fig. 11 is a block diagram of OpenFOAM "thermal-force" coupling calculation for a transient calculation method for multiple physical couplings of a heat pipe solid-state stack according to an embodiment of the present application.
As shown in fig. 11, in the multi-physical coupling transient calculation method for the heat pipe solid state stack, the OpenFOAM model includes core heat transfer and thermal expansion calculation, and heat pipe heat transfer and heat leakage of the reflective layer. And repeatedly iterating different computing modules until convergence.
In order to implement the above embodiments, the present invention further provides a computer device, which includes a memory, a processor, and a computer program stored in the memory and executable on the processor, and when the processor executes the computer program, the method for calculating multiple physical coupling transients for a heat pipe solid state stack according to the above embodiments is implemented.
In order to implement the above embodiments, the present invention further proposes a non-transitory computer-readable storage medium, on which a computer program is stored, which when executed by a processor implements the multi-physical coupling transient computing method for a heat pipe solid state stack of the above embodiments.
In the description herein, reference to the description of the term "one embodiment," "some embodiments," "an example," "a specific example," or "some examples," etc., means that a particular feature, structure, material, or characteristic described in connection with the embodiment or example is included in at least one embodiment or example of the application. In this specification, the schematic representations of the terms used above are not necessarily intended to refer to the same embodiment or example. Furthermore, the particular features, structures, materials, or characteristics described may be combined in any suitable manner in any one or more embodiments or examples. Furthermore, various embodiments or examples and features of different embodiments or examples described in this specification can be combined and combined by one skilled in the art without contradiction.
Furthermore, the terms "first", "second" and "first" are used for descriptive purposes only and are not to be construed as indicating or implying relative importance or implicitly indicating the number of technical features indicated. Thus, a feature defined as "first" or "second" may explicitly or implicitly include at least one such feature. In the description of the present application, "plurality" means at least two, e.g., two, three, etc., unless specifically limited otherwise.
Any process or method descriptions in flow charts or otherwise described herein may be understood as representing modules, segments, or portions of code which include one or more executable instructions for implementing steps of a custom logic function or process, and alternate implementations are included within the scope of the preferred embodiment of the present application in which functions may be executed out of order from that shown or discussed, including substantially concurrently or in reverse order, depending on the functionality involved, as would be understood by those reasonably skilled in the art of the present application.
The logic and/or steps represented in the flowcharts or otherwise described herein, such as an ordered listing of executable instructions that can be considered to implement logical functions, can be embodied in any computer-readable medium for use by or in connection with an instruction execution system, apparatus, or device, such as a computer-based system, processor-containing system, or other system that can fetch the instructions from the instruction execution system, apparatus, or device and execute the instructions. For the purposes of this description, a "computer-readable medium" can be any means that can contain, store, communicate, propagate, or transport the program for use by or in connection with the instruction execution system, apparatus, or device. More specific examples (a non-exhaustive list) of the computer-readable medium would include the following: an electrical connection (electronic device) having one or more wires, a portable computer diskette (magnetic device), a Random Access Memory (RAM), a read-only memory (ROM), an erasable programmable read-only memory (EPROM or flash memory), an optical fiber device, and a portable compact disc read-only memory (CDROM). Further, the computer-readable medium could even be paper or another suitable medium upon which the program is printed, as the program can be electronically captured, via for instance optical scanning of the paper or other medium, then compiled, interpreted or otherwise processed in a suitable manner if necessary, and then stored in a computer memory.
It should be understood that portions of the present application may be implemented in hardware, software, firmware, or a combination thereof. In the above embodiments, the various steps or methods may be implemented in software or firmware stored in memory and executed by a suitable instruction execution system. If implemented in hardware, as in another embodiment, any one or combination of the following techniques, which are known in the art, may be used: a discrete logic circuit having a logic gate circuit for implementing a logic function on a data signal, an application specific integrated circuit having an appropriate combinational logic gate circuit, a Programmable Gate Array (PGA), a Field Programmable Gate Array (FPGA), or the like.
It will be understood by those skilled in the art that all or part of the steps carried by the method for implementing the above embodiments may be implemented by hardware related to instructions of a program, which may be stored in a computer readable storage medium, and when the program is executed, the program includes one or a combination of the steps of the method embodiments.
In addition, functional units in the embodiments of the present application may be integrated into one processing module, or each unit may exist alone physically, or two or more units are integrated into one module. The integrated module can be realized in a hardware mode, and can also be realized in a software functional module mode. The integrated module, if implemented in the form of a software functional module and sold or used as a separate product, may also be stored in a computer-readable storage medium.
The storage medium mentioned above may be a read-only memory, a magnetic or optical disk, etc. Although embodiments of the present application have been shown and described above, it is understood that the above embodiments are exemplary and should not be construed as limiting the present application, and that variations, modifications, substitutions and alterations may be made to the above embodiments by those of ordinary skill in the art within the scope of the present application.

Claims (7)

1. A multi-physical coupling transient calculation method for a heat pipe solid state reactor is characterized in that an OpenFOAM program is used as a platform, a reactivity feedback model, a point reactor dynamics model, a heat pipe transient calculation model, a contact heat exchange model and a reactor core heat leakage model are subjected to modular design, and multi-coupling physical calculation of the heat pipe solid state reactor is realized through calling and iteration among different modules, wherein the calling and iteration among the different modules comprises the following steps:
inputting the temperature distribution of the current reactor and the heat pipe heat absorption power as input data into the reactivity feedback model for reactivity feedback calculation to obtain the total reactivity at the current moment;
calling the point reactor dynamics model, and obtaining a power time change function according to the total reactivity;
calculating according to RMC to obtain a power spatial distribution function, and updating a current power description function according to the power spatial distribution function and the power time change function to obtain an updated power description function;
determining the reactor core power distribution at the current moment by using the updated power description function, calling a heat pipe transient calculation model to perform heat transfer coupling calculation on the reactor core to obtain the reactor core temperature distribution, bringing the reactor core temperature distribution into a deformation equation containing thermal expansion, and calculating to obtain the reactor core thermal expansion calculation result;
judging whether the reactor core is in contact with the reflecting layer or not according to the calculation result of the thermal expansion of the reactor core, calling the contact heat exchange model to perform heat transfer calculation between the reactor core and the reflecting layer if the reactor core is in contact with the reflecting layer, obtaining a corresponding contact heat exchange coefficient, and updating the heat transfer quantity between the reactor core and the reflecting layer by combining the temperature of the outer surface of the reactor core and the temperature of the inner surface of the reflecting layer on the basis of the contact heat exchange coefficient;
inputting the heat transfer quantity between the reactor core and the reflecting layer into the reactor core heat leakage model as input data to calculate the heat leakage of the reflecting layer, thereby determining the heat leakage quantity between the reactor core, the reflecting layer and the environment;
calling and iterating the different modules in a circulating manner until the relative deviation of the peak temperature of the calculation domain of the two iterations is less than 1 e-5;
wherein the reactive feedback calculation is specifically represented as:
ρ(t)＝ρ0+ρext+ρD+ρF+ρH1+ρH2+ρS
Figure FDA0003596047400000011
ρF＝αF[Tf(t)-Tf(0)]，ρH1＝αH1[Th(t)-Th(0)]
ρH2＝αH2[Q(t)-Q(0)]，ρS＝αs[Tm(t)-Tm(0)]
where ρ is0For initial reactivity, pextFor external introduction of reactivity, pDFor fuel Doppler feedback reactivity, ρFFor deformation feedback reactivity, ρH1For heat pipe temperature feedback reactivity, ρH2For heat pipe power feedback reactivity, ρSFor temperature feedback reactivity of the structural material, alphaD、αF、
Figure FDA0003596047400000012
αsIs a reactive feedback coefficient;
the heat pipe transient calculation model comprises a self-diffusion model, a plane front model and a network thermal resistance model, the heat pipe is started into 3 stages, different heat pipe transient calculation models are called according to different stages to carry out heat transfer coupling calculation on the reactor core, wherein the judgment of different stages is carried out by adopting Knudsen number, Knudsen is recorded as Kn,
when Kn is more than or equal to 0.01, calling a self-diffusion model in the heat pipe transient calculation model;
when Kn is less than 0.01 and the heat pipe is not completely started, calling a plane front heat pipe model in the heat pipe transient calculation model;
when Kn is less than 0.01 and the heat pipe is completely started, calling a network thermal resistance model in the heat pipe transient calculation model,
the self-diffusion model comprises the following components: a system of thermal conductivity differential equations and self-diffusion equations, as follows:
differential equation of heat conduction:
Figure FDA0003596047400000021
wherein rho is the density of the material, C is the specific heat capacity of the material, lambda is the thermal conductivity of the material, T is the temperature of the material, T is the time,
the self-diffusion equation set comprises a mass self-diffusion equation and an energy self-diffusion equation:
mass self-diffusion equation:
Figure FDA0003596047400000022
energy self-diffusion equation:
Figure FDA0003596047400000023
wherein D isvIs the vapor self-diffusion coefficient, GrFor radially self-diffusing mass flow, GzIs the self-diffusion mass flow in the axial direction, r is a radial coordinate, z is an axial coordinate,
the plane front equation comprises a heat conduction differential equation, and also comprises a fluid continuity equation, an N-S equation and a fluid energy equation:
continuity equation:
Figure FDA0003596047400000024
axial N-S equation:
Figure FDA0003596047400000025
radial N-S equation:
Figure FDA0003596047400000026
energy equation:
Figure FDA0003596047400000027
wherein v is the radial velocity, w is the radial velocity, μ is the steam viscosity, P is the steam pressure, φ is the energy source term,
the network thermal resistance model uses a node equation to calculate the temperature:
Figure FDA0003596047400000028
wherein A is the node area, Q is the input/output energy, i is the node number;
and calculating the heat transfer between the reactor core and the reflecting layer by:
Figure FDA0003596047400000031
Hb＝min(H1，H2)，
Figure FDA0003596047400000032
wherein HiIs the hardness of the material, kiIs the thermal conductivity, σiAs surface roughness, miThe slope of the surface roughness peak, P is the contact pressure, dbIs the coefficient of the Vickers microhardness relation, hcTo contact heat transfer coefficient, HbIs the equivalent hardness of the material, H1Material 1 hardness, H2Is the hardness, k, of material 21Is the thermal conductivity, k, of the material 12Is the thermal conductivity, k, of material 2sTo equivalent thermal conductivity, σ1Is the surface roughness, σ, of the material 12Is the surface roughness, m, of the material 21The roughness of the surface of the material 1 is the slope of the peak, m2The slope of the rough peak on the surface of the material 2 is shown;
the reflective layer heat leakage calculation is expressed as:
Figure FDA0003596047400000033
where ρ is the material density of the reflective layer, cpThe specific heat capacity of the reflecting layer material is adopted, k is the material heat conductivity, Q is the volume heat source of the reflecting layer, T is the material temperature, the heat flow between the reactor core and the reflecting layer is calculated by using the gap heat transfer or contact heat exchange on the inner surface of the reflecting layer, and the convection heat exchange boundary or the radiation heat exchange boundary is adopted on the outer surface according to the actual reactor.
2. The method of claim 1, wherein the point stack dynamics model comprises a system of point stack dynamics equations expressed as:
Figure FDA0003596047400000034
Figure FDA0003596047400000035
Figure FDA0003596047400000036
wherein rho is total reactivity, beta is effective share of delayed neutrons, Λ is average generation time of prompt neutrons, and λiIs the decay constant of the precursor nucleus, C, of each group of delayed neutronsiPrecursor nuclear density, beta, of each group of delayed neutronsiThe effective portion of delayed neutrons in each group.
3. The method of claim 1, wherein said updating a current power description function based on said power spatial distribution function and said power time variation function is represented as:
P(r,t)＝K(r)×p(t)
wherein p (t) is a power time variation function, K (r) is a power space distribution function, r is a space coordinate, and t is time.
4. The method of claim 1, wherein the Knudsen number is expressed as:
Figure FDA0003596047400000041
wherein, the lambda is the calculation formula of the mean free path of the steam molecules,
Figure FDA0003596047400000042
d is the pipe diameter, TtrFor the transition temperature, the transition temperature T under different Kn numbers and pipe diameters D is calculated on the premise that the steam cavity working medium is in a saturated statetrK is a boltzmann function, P is pressure, and σ is an average collision diameter of gas molecules.
5. The method of claim 1, wherein whether the core is in contact with the reflecting layer is determined according to the core thermal expansion calculation result, if the core is not in contact with the reflecting layer, the core and the reflecting layer realize heat transfer through radiation heat exchange or gap heat conduction, and the heat transfer calculation between the core and the reflecting layer is performed by adopting a steady state radiation heat exchange formula and a steady state heat transfer formula under corresponding geometric conditions.
6. A computer device comprising a memory, a processor and a computer program stored on the memory and executable on the processor, the processor implementing the method of any one of claims 1-5 when executing the computer program.
7. A non-transitory computer-readable storage medium having stored thereon a computer program, wherein the computer program, when executed by a processor, implements the method of any one of claims 1-5.
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